In deep drawing, being able to work a product more deeply translates to higher product value. The limiting draw ratio is an index indicating the possible working depth in deep drawing. The limiting draw ratio is the ratio D/d of the raw sheet material diameter D to the limiting product diameter d that can be worked. The limiting draw ratio needs to be increased to that products can be worked more deeply. To this end, there is a warm deep drawing method in which the sheet material is heated to increase its ductility and allow a more deeply worked product to be obtained. A known example of this working technique is the following Patent Document 1. Patent Document 1 states that a sheet material is heated with an electric heater prior to performing deep drawing. The cooling of the sheet material during working is also discussed.    Patent Document 1: Japanese Patent Application Laid-Open No. H5-237558
With a technique such as that in Patent Document 1, since the sheet material is heated by electric heater from outside the sheet material, there is a considerable time lag until the sheet material is heated to the required temperature all the way through in its thickness direction. Therefore, problems that are encountered are that heating control over the sheet material is less precise, as are the shape of the final product and the sheet thickness. There is a need to be able to increase the workable depth without causing this loss of precision.